Why is my Pelican Standard Controller for PS1 not working at all?

To test the wires you will need to perform a continuity test. For that you will need a multitester/multimeter. Most of the modern ones if you put them on the lowest OHM setting will produce a sound if there is good continuity. You will need to take the controller apart. Follow where each of the wires go from the cord to the board. On each wire put one of the test probes where the wire is soldered to the board, be sure you are touching metal. Take the other test probe from the multitester and run it across the pads on the other end of the cord if you hear a sound the wire should be good. You will have to dot his for every wire. If you have one that doesn't give a sound, you found your bad wire. The only 2 wires I can think of that could cause none of the buttons to function is a ground or a voltage reference wire.